Equivariant CW complexes and shape theory
Let X be a G-space and G a discrete group. The author introduces the equivariant Čech system for X. Denoting by \({\mathcal H}_ G\) the category whose objects are G-spaces and morphisms are G-homotopy classes of G-maps, and by \({\mathcal W}_ G\) the full subcategory of \({\mathcal H}_ G\) consisting of G-spaces which have the G-homotopy types of G-CW complexes, he proves the following theorem: There is a functor Č\({}_ G: {\mathcal H}_ G\to pro\)-\({\mathcal W}_ G\) so that Č\({}_ G(X)=(X_{\lambda},[p^ X_{\lambda \lambda '}]_ G,\Lambda)\) has the universal property for the equivariant shape theory with a system G-map \(p^ X=([p^ X_{\lambda}]_ G): X\to \check C_ G(X)\), that is, \(p^ X: X\to \check C_ g(X)\) is a G-CW expansion of X. The case when G is finite is also considered. In this case any G-ANR expansion of X is equivalent to \(p^ X: X\to \check C_ G(X)\).
scientific article; zbMATH DE number 4119235